DOCSLIB.ORG

How Spatial Is Hyperspace? Interacting with Hypertext Documents: Cognitive Processes and Concepts

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
How Spatial Is Hyperspace? Interacting with Hypertext Documents: Cognitive Processes and Concepts CYBERPSYCHOLOGY & BEHAVIOR Volume 4, Number 1, 2001 Mary Ann Liebert, Inc. How Spatial Is Hyperspace? Interacting with Hypertext Documents: Cognitive Processes and Concepts PATRICIA M. BOECHLER ABSTRACT The World Wide Web provides us with a widely accessible technology, fast access to massive amounts of information and services, and the opportunity for personal interaction with nu- merous individuals simultaneously. Underlying and influencing all of these activities is our basic conceptualization of this new environment; an environment we can view as having a cognitive component (hyperspace) and a social component (cyberspace). This review argues that cognitive psychologists have a key role to play in the identification and analysis of how the processes of the mind interact with the Web. The body of literature on cognitive processes provides us with knowledge about spatial perceptions, strategies for navigation in space, memory functions and limitations, and the formation of mental representations of environ- ments. Researchers of human cognition can offer established methodologies and conceptual frameworks toward investigation of the cognitions involved in the use of electronic envi- ronments like the Web. INTRODUCTION only a new cognitive environment (“hyper- space”) where information is perceived, stored, OR CENTURIES, TEXT-BASED LITERATURE has manipulated, and retrieved in new ways, but Fbeen the primary mode for disseminating also a new social environment (“cyberspace”), and receiving information. The cognitive where one individual’s cognitions about this processes involved in reading and writing new environment interact with those of other books have been studied extensively for people who share it. Unlike physical space, the decades as they have played a crucial role in World Wide Web is not constrained by dis- the development of humankind. In the past two tance. Interactions between individuals can be decades, hypertext systems (computer-based numerous and instantaneous. The possibilities information systems of interconnected docu- for enhancing individuals’ lives through easily ments) have become increasingly pervasive in accessed personal interactions and the avail- work, home, and educational environments. ability of online services are abundant. With the advent of the World Wide Web, these The study of hypertext systems is a multi- information systems are heavily influencing disciplinary venture. Psychologists, computer how we develop as a society. However, unlike scientists, and educators all bring different ap- traditional text information sources, the World proaches and goals to the effort. Cognitive psy- Wide Web is interactive. This has created not chologists wish to know how humans concep- Psychology Department, University of Alberta, Edmonton, Alberta, Canada. 23 24 BOECHLER tualize hyperspace and the nature of the men- performance, and spatial processing. Under- tal representations they form of hyperspace. standing the cognitive aspects of hyperspace Social psychologists want to understand how will help us to develop optimal technologies this new way of communicating impacts an in- that will guide the way we use the social envi- dividual’s sense of self, their social sphere, the ronment of cyberspace. Understanding the cog- group dynamics of this new environment, and nitive processes that shape many different in- the effect on society at large in both a regional dividuals’ perceptions of hyperspace will and global sense. Clinical psychologists are in- facilitate the creation of technologies that are vestigating the ways that these systems can be accessible to a wide range of people with a used to provide psychological services. Com- wide range of characteristics (e.g., age differ- puter scientists and software developers want ences) and skills (e.g., level of literacy). For the to know how to design an optimal interface for uninitiated, traversing the World Wide Web in users. Educators are interested in how this search of solutions to everyday problems can technology can be applied to enhance learning. be extremely daunting and can often end in This can be advantageous as a broad knowl- failure to locate useful information or access edge base and diverse perspectives are brought needed services. Providing navigation tools to bear on the topic. However, it also results in that are based on the cognitive processes of the lack of a unified theoretical foundation for users will do much toward making the World hypertext. Relative to many other areas of psy- Wide Web an accessible resource for everyone. chological study, research on the cognitive as- Psychological processes are often described pects of using such systems is in its infancy; via metaphors.3,4 Hyperspace is a dynamic, in- models and paradigms are still being devel- teractive space requiring new psychological oped. metaphors, new ways of thinking and inter- One point to note is that the above-mentioned preting information. However, before we can endeavors are not as distinct as one might ini- devise new metaphors that portray this envi- tially suppose. Basic cognitive processes (e.g., ronment accurately, it is prudent to closely ex- memory, perception, etc.) are the underpin- amine previous metaphors to identify benefi- nings for more complex processes (e.g., so- cial aspects that can act as a foundation for new cial–emotional responses to our environment). metaphors. In the real world, we’ve identified many rela- One overarching metaphor seems to domi- tionships between basic cognitions and social nate the hypertext literature: the spatial responses.1,2 There are numerous instances of metaphor. The spatial metaphor arose out of a our perceptions of physical space producing need for a common language to discuss hy- psychosocial consequences (e.g., personal space pertext issues and a framework within which being violated, overcrowding, feeling lost). It is to develop usable interfaces. Its basic premise reasonable to suppose that how we perceive is that locating information in hyperspace has hyperspace may affect our social interactions similar psychological features to navigating in within it. Understanding our cognitive reac- physical space. Therefore, promoting mental tions to hyperspace may well aid us in pre- representations of spatial layouts of informa- dicting some of our social and emotional re- tion is a good approach to improving the hy- sponses to this new environment. To fully take pertext user’s ability to access information.5,6 advantage of the opportunities offered by cy- Navigational tools modeled after real-world berspace, we need to comprehend clearly how navigational aids such as maps appear to en- individuals take in information from hyper- hance performance on some measures7–11 but space. not on others.12–16 Correlational data on the re- To this end, the traditional paradigms and lationship between spatial ability and perfor- theories of cognitive psychology have much to mance has shown increases in speed of perfor- offer, providing us with established method- mance with higher spatial ability,17,18 but ologies and conceptual frameworks for explor- marginal effects on the accuracy of perfor- ing different facets of cognition relevant to hy- mance.19 Therefore, the empirical evidence to pertext navigation, such as memory, task date has not resolved the issue of how or to HOW SPATIAL IS HYPERSPACE? 25 what degree spatial processing is involved in uments that contain images, audio, and video the efficiency and effectiveness of hypertext clips are referred to as “hypermedia” docu- use. ments. In the hypermedia literature the terms The spatial metaphor seems easily under- “hypertext” and “hypermedia” are often used stood by novice users. However, if it is not an interchangeably. 20 accurate metaphor for the mental processes Each hypertext window contains icons that that humans engage in as they interact with hy- can be pictorial symbols or highlighted words pertext, or if we do not understand the aspects (hotwords). A window can contain any num- of the comparison that make the metaphor ben- ber of these icons. The icon represents the link eficial, then as more and more complex, pow- to the database for that particular piece of in- erful systems are developed this metaphor will formation. When clicked on with a pointing de- eventually be less useful. This would be so for vice (usually a mouse), the icon activates the both the goal of achieving optimal access to in- link to the referenced node in the database and formation and the goal of presenting informa- a new window is instantaneously opened con- tion in a form that can enhance social interac- taining the information in that node. Nodes tion or learning. that hold related information are linked. Some The following review draws from many di- nodes will have a multitude of links, both to verse areas of cognitive psychological study to and from other nodes based on their related- bring forth questions whose answers could ness, whereas other nodes may only have in- greatly impact the benefits we are able to gar- coming links. It is important to stress that links ner from cyberspace. It is an in-depth look at are not merely connections between nodes but the possible ways we can view the new envi- that they should specify the semantic relation- ronment of the World Wide Web. This may or ships between nodes. The author of the hyper- may not be as a space, therefore, this review text document is the engineer of the links based also critically examines the spatial metaphor on his or her semantic network; that is, his or for hypertext interaction. her conceptions of the interconnectedness of ideas within the chosen material.21,22 Links can be organized in two ways: in a hi- erarchical structure or in a network structure. AN INTRODUCTION TO HYPERTEXT In a hierarchical structure, nodes are only linked to the superordinate information above What is hypertext? them or the subordinate information below Generally, a hypertext system is an electronic them.21,23 In a network structure, any node can system of interconnected units of information be linked to any other. Multiple links can exist or text nodes.
Load more

Recommended publications
  • Interaction of the Past of Parallel Universes
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Interaction of the Past of parallel universes Alexander K. Guts Department of Mathematics, Omsk State University 644077 Omsk-77 RUSSIA E-mail: [email protected] October 26, 1999 ABSTRACT We constructed a model of five-dimensional Lorentz manifold with foliation of codimension 1 the leaves of which are four-dimensional space-times. The Past of these space-times can interact in macroscopic scale by means of large quantum fluctuations. Hence, it is possible that our Human History consists of ”somebody else’s” (alien) events. In this article the possibility of interaction of the Past (or Future) in macroscopic scales of space and time of two different universes is analysed. Each universe is considered as four-dimensional space-time V 4, moreover they are imbedded in five- dimensional Lorentz manifold V 5, which shall below name Hyperspace. The space- time V 4 is absolute world of events. Consequently, from formal standpoints any point-event of this manifold V 4, regardless of that we refer it to Past, Present or Future of some observer, is equally available to operate with her.Inotherwords, modern theory of space-time, rising to Minkowsky, postulates absolute eternity of the World of events in the sense that all events exist always. Hence, it is possible interaction of Present with Past and Future as well as Past can interact with Future. Question is only in that as this is realized. The numerous articles about time machine show that our statement on the interaction of Present with Past is not fantasy, but is subject of the scientific study.
    [Show full text]
  • A Comparison of Two Navigational Aids for Hypertext Mark Alan Satterfield Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1992 A comparison of two navigational aids for hypertext Mark Alan Satterfield Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Business and Corporate Communications Commons, and the English Language and Literature Commons Recommended Citation Satterfield, Mark Alan, "A comparison of two navigational aids for hypertext" (1992). Retrospective Theses and Dissertations. 14376. https://lib.dr.iastate.edu/rtd/14376 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. A Comparison of two navigational aids for h3q5ertext by Mark Alan Satterfield A Thesis Submitted to the Gradxiate Facultyin Partial Fulfillment ofthe Requirements for the Degree of MASTER OF ARTS Department: English Major; English (Business and Technical Communication) Signatureshave been redactedforprivacy Iowa State University Ames, Iowa 1992 Copyright © Mark Alan Satterfield, 1992. All rights reserved. u TABLE OF CONTENTS Page ACKNOWLEDGEMENTS AN INTRODUCTION TO USER DISORIENTATION AND NAVIGATION IN HYPERTEXT 1 Navigation Aids 3 Backtrack 3 History 4 Bookmarks 4 Guided tours 5 Indexes 6 Browsers 6 Graphic browsers 7 Table-of-contents browsers 8 Theory of Navigation 8 Schemas ^ 9 Cognitive maps 9 Schemas and maps in text navigation 10 Context 11 Schemas, cognitive maps, and context 12 Metaphors for navigation ' 13 Studies of Navigation Effectiveness 15 Paper vs.
    [Show full text]
  • Near-Death Experiences and the Theory of the Extraneuronal Hyperspace
    Near-Death Experiences and the Theory of the Extraneuronal Hyperspace Linz Audain, J.D., Ph.D., M.D. George Washington University The Mandate Corporation, Washington, DC ABSTRACT: It is possible and desirable to supplement the traditional neu rological and metaphysical explanatory models of the near-death experience (NDE) with yet a third type of explanatory model that links the neurological and the metaphysical. I set forth the rudiments of this model, the Theory of the Extraneuronal Hyperspace, with six propositions. I then use this theory to explain three of the pressing issues within NDE scholarship: the veridicality, precognition and "fear-death experience" phenomena. Many scholars who write about near-death experiences (NDEs) are of the opinion that explanatory models of the NDE can be classified into one of two types (Blackmore, 1993; Moody, 1975). One type of explana tory model is the metaphysical or supernatural one. In that model, the events that occur within the NDE, such as the presence of a tunnel, are real events that occur beyond the confines of time and space. In a sec ond type of explanatory model, the traditional model, the events that occur within the NDE are not at all real. Those events are merely the product of neurobiochemical activity that can be explained within the confines of current neurological and psychological theory, for example, as hallucination. In this article, I supplement this dichotomous view of explanatory models of the NDE by proposing yet a third type of explanatory model: the Theory of the Extraneuronal Hyperspace. This theory represents a Linz Audain, J.D., Ph.D., M.D., is a Resident in Internal Medicine at George Washington University, and Chief Executive Officer of The Mandate Corporation.
    [Show full text]
  • Arxiv:1902.02232V1 [Cond-Mat.Mtrl-Sci] 6 Feb 2019
    Hyperspatial optimisation of structures Chris J. Pickard∗ Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom and Advanced Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba, Sendai, 980-8577, Japan (Dated: February 7, 2019) Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy landscape. In many cases these local minima are relatively high in energy, and inspection reveals that they are trapped, tangled, or otherwise frustrated in their descent to a lower energy configuration. Strategies have been developed which attempt to overcome these traps, such as classical and quantum annealing, basin/minima hopping, evolutionary algorithms and swarm based methods. Random structure search makes no attempt to avoid the local minima, and benefits from a broad and uncorrelated sampling of configuration space. It has been particularly successful in the first principles prediction of unexpected new phases of dense matter. Here it is demonstrated that by starting the structural optimisations in a higher dimensional space, or hyperspace, many of the traps can be avoided, and that the probability of reaching low energy configurations is much enhanced. Excursions into the extra dimensions are progressively eliminated through the application of a growing energetic penalty. This approach is tested on hard cases for random search { clusters, compounds, and covalently bonded networks. The improvements observed are most dramatic for the most difficult ones. Random structure search is shown to be typically accelerated by two orders of magnitude, and more for particularly challenging systems.
    [Show full text]
  • General N-Dimensional Rotations
    General n-Dimensional Rotations Antonio Aguilera Ricardo Pérez-Aguila Centro de Investigación en Tecnologías de Información y Automatización (CENTIA) Universidad de las Américas, Puebla (UDLAP) Ex-Hacienda Santa Catarina Mártir México 72820, Cholula, Puebla [email protected] [email protected] ABSTRACT This paper presents a generalized approach for performing general rotations in the n-Dimensional Euclidean space around any arbitrary (n-2)-Dimensional subspace. It first shows the general matrix representation for the principal n-D rotations. Then, for any desired general n-D rotation, a set of principal n-D rotations is systematically provided, whose composition provides the original desired rotation. We show that this coincides with the well-known 2D and 3D cases, and provide some 4D applications. Keywords Geometric Reasoning, Topological and Geometrical Interrogations, 4D Visualization and Animation. 1. BACKGROUND arctany x x 0 arctany x x 0 The n-Dimensional Translation arctan2(y, x) 2 x 0, y 0 In this work, we will use a simple nD generalization of the 2D and 3D translations. A point 2 x 0, y 0 x (x1 , x2 ,..., xn ) can be translated by a distance vec- In this work we will only use arctan2. tor d (d ,d ,...,d ) and results x (x, x ,..., x ) , 1 2 n 1 2 n 2. INTRODUCTION which, can be computed as x x T (d) , or in its expanded matrix form in homogeneous coordinates, The rotation plane as shown in Eq.1. [Ban92] and [Hol91] have identified that if in the 2D space a rotation is given around a point, and in the x1 x2 xn 1 3D space it is given around a line, then in the 4D space, in analogous way, it must be given around a 1 0 0 0 plane.
    [Show full text]
  • Can a "Hyperspace" Really Exist? by Edward J. Zampino (August, 1997
    Can a "Hyperspace" really Exist? by Edward J. Zampino (August, 1997 ) NASA Lewis Research Center 21000 Brookpark Rd., Cleveland, Ohio 44135 (216)433-2042 [email protected] L._ _ _- Abstract The idea of "hyperspace" is suggested as a possible approach to faster-than-light (FTL) motion. A brief summary of a 1986 study on the Euclidean representation of space-time by the author is presented. Some new calculations on the relativistic momentum and energy of a free particle in Euclidean "hyperspace" are now added and discussed. The superimposed Energy-Momentum curves for subluminal particles, tachyons, and particles in Euclidean "hyperspace" are presented. It is shown that in Euclidean "hyperspace", instead of a relativistic time dilation there is a time "compression" effect. Some fundamental questions are presented. 1. INTRODUCTION In the George Lucas and 20 _hCentury Fox Production of STAR WARS, Han Solo engages a drive mechanism on the Millennium Falcon to attain the "boost-to-light-speed". The star field visible from the bridge streaks backward and out of sight as the ship accelerates to light speed. Science fiction writers have fantasized time and time again the existence of a special space into which a space ship makes a transition. In this special space, objects can exceed the speed of light and then make a transition from the special space back to "normal space". Can a special space (which I will refer to as hyperspace) exist? Our first inclination is to emphatically say nol However, what we have learned from areas of research such as Kaluza-Klein theory[l], Grand Unified supersymmetry theory [2], and Heterotic string theory [3] is that there indeed can be many types of spaces.
    [Show full text]
  • Maps and Their Place in Mesopotamia, Egypt, Greece, and Rome
    bibliography Adam, J.-P. 1994. Roman Building: Materials ———. 2005. Les routes de la navigation antique: and Techniques. Translated by A. Mathews. Itinéraires en Méditerranée. Paris: Errance. London: Batsford. ———. 2007. “Diocletian’s Prices Edict: The Aillagon, J.-J., ed. 2008. Rome and the Barbar- Prices of Seaborne Transport and the Average ians: The Birth of a New World. Milan: Skira. Duration of Maritime Travel.” Journal of Ro- Alföldy, G. 2000. Provincia Hispania Superior. man Archaeology 20:321– 36. Schriften der Philosophisch- historischen ———. 2007– 8. “Texte et carte de Marcus Klasse der Heidelberger Akademie der Agrippa: Historiographie et données tex- Wissenschaften 19. Heidelberg: Winter. tuelles.” Geographia Antiqua 16– 17:73– 126. al- Jadir, W. 1987. “Une bibliothèque et ses Arnaud- Lindet, M.-P., ed. and trans. 1993. Aide- tablettes.” Archèologia (Dijon) 224:18– 27. mémoire (Liber memorialis). By L. Ampelius. al- Karaji. 1940. Inbat al- miyah al- khafi yya. Paris: Les Belles Lettres. Hyderabad: Da’irat al- ma’arif al- ’uthmaniya. ———, ed. and trans. 1994. Abrégé des hauts faits Reprinted in F. Sezgin et al., eds., Water- du peuple romain. By Festus. Paris: Les Belles Lifting Devices in the Islamic World: Texts Lettres. and Studies, 302– 98 (Frankfurt: Institute Ashby, T. 1935. The Aqueducts of Ancient Rome. for the History of Arabic- Islamic Science, Oxford: Oxford University Press. 2001). Ashmore, W., and A. B. Knapp, eds. 1999. Andreu, G., and C. Barbotin, eds. 2002. Les Archaeologies of Landscape: Contemporary Per- artistes de Pharaon: Deir el- Médineh et la spectives. Malden, MA: Blackwell Publishers. Vallée des Rois. Turnhout: Brepols. Baines, J. 1987. Fecundity Figures.
    [Show full text]
  • Dimension Theory: Road to the Forth Dimension and Beyond
    Dimension Theory: Road to the Fourth Dimension and Beyond 0-dimension “Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality, for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.” ― Edwin A. Abbott, Flatland: A Romance of Many Dimensions 0-dimension Space of zero dimensions: A space that has no length, breadth or thickness (no length, height or width). There are zero degrees of freedom. The only “thing” is a point. = ∅ 0-dimension 1-dimension Space of one dimension: A space that has length but no breadth or thickness A straight or curved line. Drag a multitude of zero dimensional points in new (perpendicular) direction Make a “line” of points 1-dimension One degree of freedom: Can only move right/left (forwards/backwards) { }, any point on the number line can be described by one number 1-dimension How to visualize living in 1-dimension Stuck on an endless one-lane one-way road Inhabitants: points and line segments (intervals) Live forever between your front and back neighbor.
    [Show full text]
  • Visualization Complex Cognitive Networks
    2012 3rd International Conference on e-Education, e-Business, e-Management and e-Learning IPEDR vol.27 (2012) © (2012) IACSIT Press, Singapore Visualization Complex Cognitive Networks + MENG Shimin 1 1 DNAgent Lab @Youlinkme.net Co., Ltd. Wuyishan, Fujian China Abstract. Cognitive flow is the important applications of information flow, workflow, social flow after, but need to break through the difficulties in cognitive mapping and materialized. Use visualization techniques to build a simulation platform to realize cognitive schema, cognitive map, flow and other visual cognitive projection, make the invisible visible understanding, building cognitive materialized, visualization mode. Base visualize digital network technology innovation Visualization Complex Cognitive Networks (VCCN) platform, achieve "symbol, mathematical, process" visual computing architecture, and the formation of cognitive visual paradigm. Base VCCN research in human-computer system needs to establish the cognitive interface to build field of cognitive, modulation of cognitive coupled states, through the acquisition of Cognitive Symbol Sequence(CSS), and cognitive activity is mapped to VCCN. It is framed for cognitive nodes, relation, chain, flow, maps, schema, and achieved cognitive object editing, storage, switching, routing, navigation, evaluation, and cognitive flow coupling, excitation, propagation, and be the cognitive visual, functional simulation, power system studies provide new ideas, new paradigm of brain information. VCCN similar negatives shot to the brain cognitive activity with CSS, for the reconstruction of cognitive activity to provide a method. Keywords: complex networks, cognitive visualization, cognitive schema, cognitive map, cognitive symbol sequence, cognitive coupling. 1. Cognitive Flow The brain is a material, energy and information dissipation structure, brain research is to use instruments to stimulation, probe, scan of the brain material, energy, information process, and shooting, collecting data, use the data to understand brain.
    [Show full text]
  • The Dual Space
    October 3, 2014 III. THE DUAL SPACE BASED ON NOTES BY RODICA D. COSTIN Contents 1. The dual of a vector space 1 1.1. Linear functionals 1 1.2. The dual space 2 1.3. Dual basis 3 1.4. Linear functionals as covectors; change of basis 4 1.5. Functionals and hyperplanes 5 1.6. Application: Spline interpolation of sampled data (Based on Prof. Gerlach's notes) 5 1.7. The bidual 8 1.8. Orthogonality 8 1.9. The transpose 9 1.10. Eigenvalues of the transpose 11 1. The dual of a vector space 1.1. Linear functionals. Let V be a vector space over the scalar field F = R or C. Recall that linear functionals are particular cases of linear transformation, namely those whose values are in the scalar field (which is a one dimensional vector space): Definition 1. A linear functional on V is a linear transformation with scalar values: φ : V ! F . A simple example is the first component functional: φ(x) = x1. We denote φ(x) ≡ (φ; x). Example in finite dimensions. If M is a row matrix, M = [a1; : : : ; an] n where aj 2 F , then φ : F ! F defined by matrix multiplication, φ(x) = Mx, is a linear functional on F n. These are, essentially, all the linear func- tionals on a finite dimensional vector space. Indeed, the matrix associated to a linear functional φ : V ! F in a basis BV = fv1;:::; vng of V , and the (standard) basis f1g of F is the row vector (1) [φ1; : : : ; φn]; where φj = (φ; vj) 1 2 BASED ON NOTES BY RODICA D.
    [Show full text]
  • Physics of the Hyperspace
    Visionary sciences The need for higher Physics of the dimensions In order to get closer to his target, na- mely to create a unified quantum field theory, Burkhard Heim initially con- centrated on gravitation. According hyperspace to Einstein´s formula E= mc2, every energy has a mass and thus, every en- ergy field is tainted with a so-called Burkhard Heim‘s fieldtheory field mass. Therefore, the gravitatio- nal field of a mass also has some ener- and radionics gy which in turn corresponds to a mass. In turn, a gravitational field emanates More than thirty years ago, the physicist from this field mass. Newton and Ein- stein neglected this field mass in their Burkhard Heim succeeded in conceptualizing the individual gravitational theories and existence of higher dimensions in mathematical could therefore work with relatively formulas. According to Heim, the entire physics of simple approximation formulas. Bur- khard Heim was the first physicist who gravitation is only possible in a twelve-dimensional consistently integrated this field mass hyperspace that mathematically illustrates the in his model. He called the resulting tangible and the mental reality. Marcus Schmieke, gravitational formula a „transcenden- tal equation“ - an equation that has no who was personally introduced by Burkhard Heim generally valid solution that encom- to cosmology, explains Heim‘s field theory and its passes all scales of the universe. One is only able to derive various approxi- consequences for radionics. mation formulas for different magni- tude ranges of the cosmos. By Marcus Schmieke, Berlin. In the macroscopic range of medium distances, the solution of Heim´s tran- scendental equation substantially cor- responds to Newton‘s law of universal he twelve dimensions are divi- vels of existence.
    [Show full text]
  • A Recursive Algorithm for the K-Face Numbers of Wythoffian-N-Polytopes Constructed from Regular Polytopes
    Journal of Information Processing Vol.25 528–536 (Aug. 2017) [DOI: 10.2197/ipsjjip.25.528] Invited Paper A recursive Algorithm for the k-face Numbers of Wythoffian-n-polytopes Constructed from Regular Polytopes Jin Akiyama1,a) Sin Hitotumatu2 Motonaga Ishii3,b) Akihiro Matsuura4,c) Ikuro Sato5,d) Shun Toyoshima6,e) Received: September 6, 2016, Accepted: May 25, 2017 Abstract: In this paper, an n-dimensional polytope is called Wythoffian if it is derived by the Wythoff construction from an n-dimensional regular polytope whose finite reflection group belongs to An,Bn,Cn,F4,G2,H3,H4 or I2(p). Based on combinatorial and topological arguments, we give a matrix-form recursive algorithm that calculates the num- ber of k-faces (k = 0, 1,...,n) of all the Wythoffian-n-polytopes using Schlafli-Wytho¨ ff symbols. The correctness of the algorithm is reconfirmed by the method of exhaustion using a computer. Keywords: Wythoff construction, Wythoffian polytopes, k-face numbers, recursive algorithm, Coxeter group ( c ) volumes and surface areas. 1. Introduction Our purpose has been completed and already implemented High-dimensional polytopes have been studied mainly by the as computer programs. We will introduce a new methodology following methodologies: to study volumes, surface areas, number of k-faces sharing a (1) Combinatorics and Topology, (2) Graph Theory, (3) Group vertex, etc. of Wythoffian-n-polytopes constructed from regular Theory and (4) Metric Geometry. See [1], [2], [8], [9], [10], [11], polytopes in the forthcoming papers. In this paper, as a first [14], [15], [18], [19] for some background researches on tilings, step, we develop a recursive algorithm that computes the f-vector lattices and polytopes.
    [Show full text]